混合不连续的Galerkin方法用于多尺度问题的超标线性博尔兹曼运输方程
Qizheng Sun1,2, Xiaojing Liu1,2, Xiang Chai1,2
1Shanghai Jiao Tong University, School of Nuclear Science and Engineering, Shanghai 200240, China.
Physical review. E
|February 7, 2025
概括
我们介绍了一种上风混合不连续的加勒金 (HDG) 方法来解决线性博尔兹曼运输方程. 这种新方法提高了多尺度和厚度扩散场景中的计算效率和准确性.
科学领域:
- 计算物理学的计算物理.
- 数字分析 数字分析
- 运输现象是运输现象.
背景情况:
- 线性博尔兹曼运输方程对于模拟各种物理现象至关重要.
- 现有的数值方法在有效处理多尺度和厚的扩散模式方面面临挑战.
研究的目的:
- 开发一种新的数值方法,用于一阶超标线性博尔兹曼运输方程.
- 在复杂的物理场景中提高模拟效率和准确性.
主要方法:
- 建议使用混合不连续的加勒金 (HDG) 方法,利用原始变量和数值痕迹.
- 该方法使用投影矩阵,并从数值痕迹构建全球矩阵系统,以减少自由度.
- 一个逆风扫描序列用于有效地解决由此产生的块-下-三角矩阵系统.
主要成果:
- 上风-高度高压法在空间顺序选择方面表现出灵活性.
- 在厚的扩散极限中进行的非对称分析表明,收与响应矩阵L有关.
- 数字实验证实了上风-高压高压的准确性和稳定性,在具有挑战性的系统中表现优于均等的高压高压.
结论:
- 提议的上风-高压高频法对于厚的扩散和多尺度异质问题是准确和稳定的.
- 该方法通过减少自由度并实现高效的解决方案策略,提供了显著的计算优势.
- 这项工作为先进的运输现象模拟提供了强大的数值工具.
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